Industry has been manufacturing container closures for many years that include an applicator for applying contents within a container, especially when the container holds a solvent or other liquid. For instance, polyester dauber brushes are often combined with closures in order for the user to apply polyvinyl chloride cement for a particular purpose. However, newer substances are continually being developed that having viscosities and material properties that differ from older products and, as a result, a user has issues applying these new substances using the known applicators that are currently available. Often the known applicators either fail to retain or properly apply newer substances for their intended purpose. Therefore, there is a need to develop a container closure with applicator that can properly apply newer substances for their intended purpose.